1,026 research outputs found
On Urabe's criteria of isochronicity
We give a short proof of Urabe's criteria for the isochronicity of periodical
solutions of the equation . We show that apart from the
harmonic oscillator there exists a large family of isochronous potentials which
must all be non-polynomial and not symmetric (an even function of the
coordinate x).Comment: 8 page
Some combinatorial problems
AbstractThere are many interesting and sophisticated problems posed in the IMO, Putnam and domestic Olympiads. Some of these problems have deep mathematical background, nice generalizations, and lead to new areas of research in combinatorics. We investigate several topics in this category and mention some results and open problems
The North Fiji basin basalts and their magma sources : Part 2. Sr-Nd isotopic and trace element constraints
RELATIONSHIP BETWEEN ANTERIOR TIBIAL TRANSLATION AND ISOMETRIC STRENGTH IN FEMALE ATHLETES
The purpose of this study was to determine whether the isometric strength of the muscles around the knee and hip is associated with anterior tibial translation. Forty-four female high school basketball players participated in this study. Anterior tibial translation was measured with a Kneelax 3 arthrometer. The isometric strengths of knee flexion, knee extension, and hip abduction were determined with a hand-held dynamometer. In the case of both the legs, significant correlations were found between the anterior tibial translation, knee extension strength, and hamstring/quadriceps strength (H/Q) ratio. No significant correlations were found between the anterior tibial translation and the knee flexion and hip abduction strengths. Muscle imbalance between the quadriceps and hamstring muscles may lead to greater anterior tibial translation
Bubbles, clusters and denaturation in genomic DNA: modeling, parametrization, efficient computation
The paper uses mesoscopic, non-linear lattice dynamics based
(Peyrard-Bishop-Dauxois, PBD) modeling to describe thermal properties of DNA
below and near the denaturation temperature. Computationally efficient notation
is introduced for the relevant statistical mechanics. Computed melting profiles
of long and short heterogeneous sequences are presented, using a recently
introduced reparametrization of the PBD model, and critically discussed. The
statistics of extended open bubbles and bound clusters is formulated and
results are presented for selected examples.Comment: to appear in a special issue of the Journal of Nonlinear Mathematical
Physics (ed. G. Gaeta
Destabilization of dark states and optical spectroscopy in Zeeman-degenerate atomic systems
We present a general discussion of the techniques of destabilizing dark
states in laser-driven atoms with either a magnetic field or modulated laser
polarization. We show that the photon scattering rate is maximized at a
particular evolution rate of the dark state. We also find that the atomic
resonance curve is significantly broadened when the evolution rate is far from
this optimum value. These results are illustrated with detailed examples of
destabilizing dark states in some commonly-trapped ions and supported by
insights derived from numerical calculations and simple theoretical models.Comment: 14 pages, 10 figure
A study of 15N14N isotopic exchange over cobalt molybdenum nitrides
The 14N/15N isotopic exchange pathways over Co3Mo3N, a material of interest as an ammonia synthesis catalyst and for the development of nitrogen transfer reactions, have been investigated. Both the homomolecular and heterolytic exchange processes have been studied, and it has been shown that lattice nitrogen species are exchangeable. The exchange behavior was found to be a strong function of pretreatment with ca. 25% of lattice N atoms being exchanged after 40 min at 600 °C after N2 pretreatment at 700 °C compared to only 6% following similar Ar pretreatment. This observation, for which the potential contribution of adsorbed N species can be discounted, is significant in terms of the application of this material. In the case of the Co6Mo6N phase, regeneration to Co3Mo3N under 15N2 at 600 °C occurs concurrently with 14N15N formation. These observations demonstrate the reactivity of nitrogen in the Co–Mo–N system to be a strong function of pretreatment and worthy of further consideration
Fluctuation of the Top Location and Avalanches in the Formation Process of a Sandpile
We investigate the formation processes of a sandpile using numerical
simulation. We find a new relation between the fluctuation of the motion of the
top and the surface state of a sandpile. The top moves frequently as particles
are fed one by one every time interval T. The time series of the top location
has the power spectrum which obeys a power law, S(f)~f^{\alpha}, and its
exponent \alpha depends on T and the system size w. The surface state is
characterized by two time scales; the lifetime of an avalanche, T_{a}, and the
time required to cause an avalanche, T_{s}. The surface state is fluid-like
when T_{a}~T_{s}, and it is solid-like when T_{a}<<T_{s}. Our numerical results
show that \alpha is a function of T_{s}/T_{a}.Comment: 15 pages, 13 figure
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